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Early Voltage in MOSFETs

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- Due to channel length modulation:

Brad Noble

Chapter 3 Slides

- Vpinchoff = VDS,sat = VGS – VTH
- Separates resistive from saturation region

- The drain current is given by
- Solving for VDS,sat:
- Good to solve for quiescent voltage-current.

Brad Noble

Chapter 3 Slides

Brad Noble

Chapter 3 Slides

Cox

Gate oxidecapacitance

inversionlayer

Depletion cap,function of x

Cdep

- We assume VTH is constant across channel
THIS IS NOT TRUE!

- Depletion region is thick at S and thin at D.

Brad Noble

Chapter 3 Slides

- PFETs typically have a shape factor 3 or 4 times larger than NFETs
- Body effect can be eliminated in PFETs by tying the n-well to VDD
- Need 6m spacing between n-wells to isolate.
- Dr. Engel always does this on input devices, not always elsewhere.

Brad Noble

Chapter 3 Slides

- What really happens if VGS < VTN?
- In digital design, IDS = 0.
- We call it “weak inversion” or W.I.
- IDS is primarily due to Idrift in strong inversion and Idiffusion in weak inversion.

Brad Noble

Chapter 3 Slides

- IDS = Idrift + Idiffusion
- If VGS > VTN the channel has been inverted.
- To be more precise, we can say the channel has been “strongly inverted” (S.I.) due to an abundance of carriers in the channel.
- Inversion is independent of whether the FET is in the linear or saturation region.

Brad Noble

Chapter 3 Slides

- Drain is more reverse biased than source:
- To find Idiff, compute gradient
- Because no carriers are lost as they travel from S to D, current is the same for all x and gradient is not a function of x.
- Note: This is not really true due to recombination, but its close!

Brad Noble

Chapter 3 Slides

Brad Noble

Chapter 3 Slides

Brad Noble

Chapter 3 Slides

- S must be big for device to be useful.
- If VDS = 100mV, can be neglected.
- For W.I. vDS,Sat 100mV
- Looks like a BJT

Brad Noble

Chapter 3 Slides

- Let
- Shape factor as a function of :
Lets you chose shape to match inversion mode.

Brad Noble

Chapter 3 Slides

Brad Noble

Chapter 3 Slides

Brad Noble

Chapter 3 Slides

Question: How many digits are significant?

Brad Noble

Chapter 3 Slides

- Suppose the previous circuit is the input device of an amplifier.
- Small-signal model holds as long as the deviations are small

Brad Noble

Chapter 3 Slides

- Taking a Taylor expansion of one variable:

Brad Noble

Chapter 3 Slides

Brad Noble

Chapter 3 Slides

Brad Noble

Chapter 3 Slides

Brad Noble

Chapter 3 Slides

Brad Noble

Chapter 3 Slides

- What is gm for a weakly inverted FET?
- What is gm for a moderately inverted FET?

Not in textbooks!

Brad Noble

Chapter 3 Slides